# Math 1022 Trigonometry Topics

**An Introduction to Angles: Degree and Radian Measure **

- Understanding degree measure and radian measure
- Converting between degree measure and radian measure
- Finding coterminal angles using degree measure and radian measure

**Applications of Radian Measure **

- Determining the area of a sector of a circle
- Determining the arc length of a sector of a circle

**Triangles (Review)**

- Classifying triangles
- Using the Pythagorean Theorem
- Understanding similar triangles
- Understanding the special right triangles

**Right Triangle Trigonometry**

- Understanding the right triangle definitions of the trigonometric functions
- Using the special right triangles
- Understanding the fundamental trigonometric identities
- Understanding cofunctions
- Evaluating trigonometric functions using a calculator

**Trigonometric Functions of General Angles**

- Understanding the four families of special angles
- Understanding the definitions of the trigonometric functions of general angles
- Finding the values of the trigonometric functions of quadrantal angles
- Understanding the signs of the trigonometric functions
- Determining reference angles
- Evaluating trigonometric functions of angles belonging to the $\frac{\pi}{3}$, $\frac{\pi}{4}$, and $\frac{\pi}{6}$ families

**The Unit Circle **

- Understanding the definition of the unit circle
- Understanding the unit circle definitions of the trigonometric functions

**The Graphs of the Trigonometric Functions**

- Understanding the graphs of the sine, cosine, tangent, cotangent, secant, and cosecant functions and their properties
- Sketching graphs of the form y=Asin(Bx-C)+D or y=Acos(Bx-C)+D
- Sketching graphs of the form y=Atan(Bx-C)+D or y=Acot(Bx-C)+D
- Sketching graphs of the form y=Asec(Bx-C)+D or y=Acsc(Bx-C)+D
- Determine the equation of a function of the form y=Asin(Bx-C) or y=Acos(Bx-C) given its graph

**Inverse Trigonometric Functions**

- Understanding and finding the exact and approximate values of the inverse sine function, the inverse cosine function, and the inverse tangent function
- Evaluating composite functions involving inverse trigonometric functions of the forms $f∘f^{-1}$, $f^{-1}∘f$, $f∘g^{-1}$, and $f^{-1}∘g$

**Trigonometric Identities**

- Substituting known identities to verify an identity
- Changing to sines and cosines to verify an identity
- Factoring to verify an identity
- Separating a single quotient into multiple quotients to verify an identity
- Combining fractional expressions to verify an identity
- Multiplying by conjugates to verify an identity

**The Sum and Difference Formulas**

- Understanding and using the sum and difference formulas for the cosine, sine, and tangent functions
- Using the sum and difference formulas to verify identities
- Using the sum and difference formulas to evaluate expressions involving inverse trigonometric functions

**The Double-Angle and Half-Angle Formulas **

- Understanding and using the double-angle formulas and the half-angle formulas
- Using the double-angle and half-angle formulas to verify identities
- Using the double-angle and half-angle formulas to evaluate expressions involving inverse trigonometric functions

**Trigonometric Equations**

- Solving trigonometric equations that are linear or quadratic in form
- Solving trigonometric equations using identities
- Solving other types of trigonometric equations
- Solving trigonometric equations using a calculator

**Right Triangle Applications**

- Solving right triangles
- Solving applications using right triangles

**The Law of Sines **

- Determining if the Law of Sines can be used to solve an oblique triangle
- Using the Law of Sines to solve the SAA case or the ASA case
- Using the Law of Sines to solve the SSA (Ambiguous) case
- Using the Law of Sines to solve applied problems involving oblique triangles

**The Law of Cosines**

- Determining if the Law of Cosines can be used to solve an oblique triangle
- Using the Law of Cosines to solve the SAS case
- Using the Law of Cosines to solve the SSS case
- Using the Law of Cosines to solve applied problems involving oblique triangles

**Area of Triangles **

- Determining the area of oblique triangles
- Using Heron’s Formula to determine the area of an SSS triangle
- Solving applied problems involving the area of triangles

**Polar Coordinates and Polar Equations**

- Plotting points using polar coordinates
- Determining different representations of a point (r, θ)
- Converting points from polar to rectangular coordinates and from rectangular to polar coordinates
- Converting equations from rectangular to polar form and from polar to rectangular form

**Graphing Polar Equations**

- Sketching equations of the form $r\cosθ = a$, $r\sinθ = a$, $ar\cosθ + br\sinθ = c$, and $θ = α$
- Sketching equations of the form $r = a$, $r = a\sinθ$, and $r = a\cosθ$
- Sketching equations of the form $r = a + b\sinθ$ and $r = a + b\cosθ$
- Sketching equations of the form $r = a\sin(nθ)$ and $r = a\cos(nθ)$
- Sketching equations of the form $r^{2} = a^{2}\sin(2θ)$ and $r^{2} = a^{2}\cos(2θ)$

**Vectors **

- Understanding the geometric representation of a vector
- Understanding operations on vectors represented geometrically
- Understanding vectors in terms of components
- Understanding vectors in terms of
**i**and**j** - Finding a unit vector
- Determining the direction angle of a vector
- Representing a vector in terms of
**i**and**j**given its magnitude and direction angle - Using vectors to solve applied problems involving velocity